We wish to find a minimum cut in \(R_n(I)\)  as this will allow us to calculate the maximum weight closed subset of \(R_p(I)\) .
By the Max Flow-Min Cut Theorem [1]}, we need only find a maximum flow through \(R_n(I)\)  in order to find a minimum cut in \(R_n(I)\) . [2]} used the Sleator-Tarjan algorithm [3]} to find a maximum flow. This algorithm completes when no augmenting path exists in \(R_n(I)\)  with respect to the final flow. Several analogous definitions used in the Sleator-Tarjan algorithm are required when we move to a combinatorial approach and so are described below.
